Class 12

22. Matrices and Determinants question bank (Maths)

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Q1.

The system of linear equations:
x + y + z = 2
2x + 3y + 2z = 5
2x + 3y + (a^2 - 1)z = a + 1

The parameter \(a\) is:

(A)

is inconsistent when \( a = 4 \)

(B)

has a unique solution for \( |a| = \sqrt{3} \)

(C)

has infinitely many solutions for \( a = 4 \)

(D)

is inconsistent when \( |a| = \sqrt{3} \)

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Q2.

If \( A = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} \), then the matrix \( A^{-50} \) when \( \theta = \frac{\pi}{12} \) is equal to:

(A)

\( \begin{bmatrix} \frac{1}{2} & -\frac{\sqrt{3}}{2} \\ \frac{\sqrt{3}}{2} & \frac{1}{2} \end{bmatrix} \)

(B)

\( \begin{bmatrix} \frac{\sqrt{3}}{2} & -\frac{1}{2} \\ \frac{1}{2} & \frac{\sqrt{3}}{2} \end{bmatrix} \)

(C)

\( \begin{bmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \end{bmatrix} \)

(D)

\( \begin{bmatrix} \frac{1}{2} & \frac{\sqrt{3}}{2} \\ -\frac{\sqrt{3}}{2} & \frac{1}{2} \end{bmatrix} \)

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